{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from scipy.stats import poisson\n",
    "\n",
    "# maximum # of cars in each location\n",
    "MAX_CARS = 20\n",
    "\n",
    "# maximum # of cars to move during night\n",
    "MAX_MOVE_OF_CARS = 5\n",
    "\n",
    "# expectation for rental requests in first location\n",
    "RENTAL_REQUEST_FIRST_LOC = 3\n",
    "\n",
    "# expectation for rental requests in second location\n",
    "RENTAL_REQUEST_SECOND_LOC = 4\n",
    "\n",
    "# expectation for # of cars returned in first location\n",
    "RETURNS_FIRST_LOC = 3\n",
    "\n",
    "# expectation for # of cars returned in second location\n",
    "RETURNS_SECOND_LOC = 2\n",
    "\n",
    "DISCOUNT = 0.9\n",
    "\n",
    "# credit earned by car\n",
    "RENTAL_CREDIT = 10\n",
    "\n",
    "# cost of moving a car\n",
    "MOVE_CAR_COST = 2\n",
    "\n",
    "# all possible actions\n",
    "actions = np.arange(-MAX_MOVE_OF_CARS, MAX_MOVE_OF_CARS + 1)\n",
    "\n",
    "\n",
    "# An up bound for poisson distribution\n",
    "# If n is greater than this value, then the probability of getting n is truncated to 0\n",
    "POISSON_UPPER_BOUND = 11\n",
    "\n",
    "# Probability for poisson distribution\n",
    "# @lam: lambda should be less than 10 for this function\n",
    "poisson_cache = dict()\n",
    "\n",
    "def poisson_probability(n, lam):\n",
    "    global poisson_cache\n",
    "    key = n * 10 + lam\n",
    "    if key not in poisson_cache:\n",
    "        poisson_cache[key] = poisson.pmf(n, lam)\n",
    "    return poisson_cache[key]\n",
    "\n",
    "def expected_return(state, action, state_value, constrant_returned_cars):\n",
    "    returns = 0.0\n",
    "    returns -= MOVE_CAR_COST * abs(action)\n",
    "\n",
    "    NUM_OF_CARS_FIRST_LOC = min(state[0] - action, MAX_CARS)\n",
    "    NUM_OF_CARS_SECOND_LOC = min(state[1] + action, MAX_CARS)\n",
    "\n",
    "    for rental_request_first_loc in range(POISSON_UPPER_BOUND):\n",
    "        for rental_request_second_loc in range(POISSON_UPPER_BOUND):\n",
    "            prob = poisson_probability(rental_request_first_loc, RENTAL_REQUEST_FIRST_LOC) * \\\n",
    "                poisson_probability(rental_request_second_loc, RENTAL_REQUEST_SECOND_LOC)\n",
    "            \n",
    "            num_of_cars_first_loc = NUM_OF_CARS_FIRST_LOC\n",
    "            num_of_cars_second_loc = NUM_OF_CARS_SECOND_LOC\n",
    "\n",
    "            valid_rental_first_loc = min(num_of_cars_first_loc, rental_request_first_loc)\n",
    "            valid_rental_second_loc = min(num_of_cars_second_loc, rental_request_second_loc)\n",
    "\n",
    "            reward = (valid_rental_first_loc + valid_rental_second_loc) * RENTAL_CREDIT\n",
    "            num_of_cars_first_loc -= valid_rental_first_loc\n",
    "            num_of_cars_second_loc -= valid_rental_second_loc\n",
    "\n",
    "            if constrant_returned_cars:\n",
    "                returned_cars_first_loc = RETURNS_FIRST_LOC\n",
    "                returned_cars_second_loc = RETURNS_SECOND_LOC\n",
    "                num_of_cars_first_loc = min(num_of_cars_first_loc + returned_cars_first_loc, MAX_CARS)\n",
    "                num_of_cars_second_loc = min(num_of_cars_second_loc + returned_cars_second_loc, MAX_CARS)\n",
    "                returns += prob * (reward + DISCOUNT * state_value[num_of_cars_first_loc, num_of_cars_second_loc])\n",
    "            else:\n",
    "                for returned_cars_first_loc in range(POISSON_UPPER_BOUND):\n",
    "                    for returned_cars_second_loc in range(POISSON_UPPER_BOUND):\n",
    "                        prob_return = poisson_probability(\n",
    "                            returned_cars_first_loc, RETURNS_FIRST_LOC\n",
    "                        ) * poisson_probability(returned_cars_second_loc, RETURNS_SECOND_LOC)\n",
    "                        num_of_cars_first_loc_ = min(num_of_cars_first_loc + returned_cars_first_loc, MAX_CARS)\n",
    "                        num_of_cars_second_loc_ = min(num_of_cars_second_loc + returned_cars_second_loc, MAX_CARS)\n",
    "                        prob_ = prob_return * prob\n",
    "                        returns += prob_ * (reward + DISCOUNT *\n",
    "                                            state_value[num_of_cars_first_loc_, num_of_cars_second_loc_])\n",
    "    return returns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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",
      "text/plain": [
       "<Figure size 4000x2000 with 12 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "def figure_4_2(constant_returned_cars=True):\n",
    "    value = np.zeros((MAX_CARS + 1, MAX_CARS + 1))\n",
    "    policy = np.zeros(value.shape, dtype=np.int32)\n",
    "\n",
    "    iterations = 0\n",
    "    _, axes = plt.subplots(2, 3, figsize=(40, 20))\n",
    "    plt.subplots_adjust(wspace=0.1, hspace=0.2)\n",
    "    axes = axes.flatten()\n",
    "    while True:\n",
    "        fig = sns.heatmap(np.flipud(policy), cmap=\"YlGnBu\", ax=axes[iterations])\n",
    "        fig.set_ylabel('# cars at first location', fontsize=30)\n",
    "        fig.set_yticks(list(reversed(range(MAX_CARS + 1))))\n",
    "        fig.set_xlabel('# cars at second location', fontsize=30)\n",
    "        fig.set_title('policy {}'.format(iterations), fontsize=30)\n",
    "\n",
    "        # policy evaluation (in-place)\n",
    "        while True:\n",
    "            old_value = value.copy()\n",
    "            for i in range(MAX_CARS + 1):\n",
    "                for j in range(MAX_CARS + 1):\n",
    "                    new_state_value = expected_return([i, j], policy[i, j], value, constant_returned_cars)\n",
    "                    value[i, j] = new_state_value\n",
    "            max_value_change = abs(old_value - value).max()\n",
    "            print('max value change {}'.format(max_value_change))\n",
    "            if max_value_change < 1e-4:\n",
    "                break\n",
    "\n",
    "        # policy improvement\n",
    "        policy_stable = True\n",
    "        for i in range(MAX_CARS + 1):\n",
    "            for j in range(MAX_CARS + 1):\n",
    "                old_action = policy[i, j]\n",
    "                action_returns = []\n",
    "                for action in actions:\n",
    "                    if (0 <= action <= i) or (-j <= action <= 0):\n",
    "                        action_returns.append(expected_return([i, j], action, value, constant_returned_cars))\n",
    "                    else:\n",
    "                        action_returns.append(-np.inf)\n",
    "                new_action = actions[np.argmax(action_returns)]\n",
    "                policy[i, j] = new_action\n",
    "                if policy_stable and old_action != new_action:\n",
    "                    policy_stable = False\n",
    "        print('policy stable {}'.format(policy_stable))\n",
    "\n",
    "        if policy_stable:\n",
    "            fig = sns.heatmap(np.flipud(value), cmap=\"YlGnBu\", ax=axes[-1])\n",
    "            fig.set_ylabel('# cars at first location', fontsize=30)\n",
    "            fig.set_yticks(list(reversed(range(MAX_CARS + 1))))\n",
    "            fig.set_xlabel('# cars at second location', fontsize=30)\n",
    "            fig.set_title('optimal value', fontsize=30)\n",
    "            break\n",
    "\n",
    "        iterations += 1\n",
    "figure_4_2()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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